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Beyond Beer's Law: Spectral Mixing Rules
Thomas G Mayerhöfer1,2, Jürgen Popp1,2
1Leibniz Institute of Photonic Technology (IPHT), Jena, Germany.
Applied Spectroscopy
|June 27, 2020
Summary
The linear mixing rule for absorbance is an approximation valid only under specific conditions, not always true for mixtures. This study derives the linear rule from the Lorentz-Lorenz relation, clarifying its limitations and alternative rules for different sample types.
Area of Science:
- Optics and Spectroscopy
- Materials Science
- Physical Chemistry
Background:
- Beer's Law assumes linear mixing of absorbances in mixtures.
- This assumption simplifies understanding mixture optical properties.
- Previous studies have not fully explored the conditions for this approximation.
Purpose of the Study:
- To investigate the validity of the linear mixing rule for absorbance.
- To derive the linear mixing rule from fundamental optical relations.
- To differentiate between various mixing rules based on approximations.
Main Methods:
- Derivation of the linear mixing rule from the Lorentz-Lorenz relation.
- Analysis of approximations leading to different mixing rules (Newton-Laplace, Gladstone-Dale/Arago-Biot).
- Illustration of spectral differences using examples for micro-homogeneous and micro-heterogeneous samples.
Main Results:
- The linear mixing rule is an approximation valid under specific conditions, including homogeneous mixing and consistent refractive indices.
- Different levels of approximation lead to distinct mixing rules.
- Micro-heterogeneous samples exhibit different mixing rules based on reflectance and transmittance, showing band flattening at high concentrations.
Conclusions:
- The linear mixing rule's applicability is limited and depends on sample homogeneity and optical properties.
- Understanding these limitations is crucial for accurate spectral analysis of mixtures.
- Alternative mixing rules are necessary for micro-heterogeneous systems.
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